Wideband Electrically Controlled Vernier Frequency Tunable Terahertz Quantum Cascade Laser

: Frequency tuning in terahertz frequency quantum cascade lasers is challenging because of low thermal and current tuning coe ﬃ cients. Moreover, photonic designs like Vernier selection based sampled gratings, used in telecom lasers to tune emission frequency, are unsuitable due to the long terahertz wavelengths and will require impractically long cavities (>15 mm). Here, we report the ﬁ rst wideband frequency tuning from a monolithic device exploiting Vernier selection rules using a coupled-cavity laser with a defect engineered photonic lattice. A precisely positioned defect lattice allows us to engineer the free spectral range and ﬁ nesse of one of the cavities, similar to a sampled grating but using shorter cavity lengths (<4 mm). A coupled-cavity was used to tune the emission frequency. We achieve frequency tuning over 209 GHz, including mode hop-free continuous tuning of ∼ 6 − 21 GHz across six frequency bands, controlled through Stark shift, cavity-pulling, localized Joule heating, and thermal e ﬀ ects.

T erahertz frequencies, typically referred to as the frequencies in the range 100 GHz to 10 THz, have wide range of potential applications, such as noninvasive screening, microscopy, biological sensing, medical imaging, material analysis, metrology, communications, defense, and security. 1 Advances in terahertz frequency quantum cascade lasers (QCLs) 2 over the last two decades have great potential in many of these areas. Compared to other terahertz sources, such as resonant tunneling diodes 3 and unitraveling-carrier photodiodes, these lasers offer superior performance such as multi-Watt output power, 4 ultrabroadband gain, 5,6 wide frequency range of operation (∼1.2−5.6 THz), 7,8 frequency comb operation, 9 and ultrashort pulse generation. 10 Like most lasers, a typical QCL waveguide uses a Fabry− Peŕot resonator and emits radiation at multiple cavity modes. This multimode emission property of terahertz QCLs has enabled their transition into applications such as comb spectroscopy, 9,11 but also restricts their use on other applications such as gas spectroscopy, 12,13 which require a frequency-tunable and single-mode source. Patterning of photonic structures onto the ridge waveguide has led to the realization of single-mode emission in terahertz lasers through the use of distributed feedback lattices, 14−17 photonic crystals, 18, 19 and finite defect site photonic lattices. 20,21 However, tuning single mode emission in QCLs has been very difficult to achieve, restricted to a hop-free continuous frequency coverage of a maximum of ∼30 GHz, 19 limited by the weak electron plasma and band-filling effects responsible for control of the refractive index. 22 The inherent limited current and thermal tuning coefficients in terahertz QCLs has led to the development of a number of frequency tuning techniques using external optics, 23 aperiodic lattices, 24 coupled micromirrors, 25,26 microelectromechanical actuators, 27 gas and dielectric deposition, 28,29 and facet heating. 30 However, the complex electromechanical control in some of these tuning approaches severely limits integration of the terahertz lasers into compact instrumentation systems. A terahertz laser with a monolithically integrated, electrically controlled, tuning mechanism remains an important goal for these lasers and would increase the speed of tuning, in addition to reduced system complexity and footprint.
At shorter wavelengths, lasers based on the Vernier selection of frequency are widely in telecom lasers 31 and, more recently, in mid-infrared QCLs 32 to electrically tune emission frequencies over a wide bandwidth from a monolithic device. Recently, electrically controlled frequency tuning has been realized from terahertz QCLs exploiting Vernier selection using coupled-cavities. 33−35 These lasers comprise two monolithically integrated cavities on the same substrate, which are optically coupled but electrically isolated through a narrow air gap. Each cavity supports a frequency comb of longitudinal modes; frequency selection in such lasers is governed by the alignment between these combs. The aligned mode experiences the lowest lasing threshold, and lasing is therefore selectively favored at that frequency ( Figure 1a). The emission frequency is tuned through an index perturbation in the coupled-cavities. However, the mode-spacing, line width and finesse of the combs in the individual cavities are restricted by the cavity dimensions in these simple designs, limiting tuning ranges. Alternatively, a complete control of comb parameters and wideband tuning can be designed using sampled-grating distributed Bragg reflectors (SG-DBRs), widely used in telecom lasers where they are used to achieve full coverage of the gain bandwidth through a combination of mode-hops and continuous tuning. 36 These designs are comprised of a few sections of a burst or chirped lattice on either side of a gain and a phase matching section ( Figure 1b). Comb parameters, such as frequency separation and finesse, are controlled by optimizing the pitch, number of bursts, and the periodicity of the SG-DBR. A direct replication of SG-DBR Vernier designs at terahertz frequencies is not feasible because of the long wavelengths, requiring impractically long cavities extending over tens of millimeters. Instead, terahertz SG-DBRs have been applied only to single cavity QCLs and are optimized for single mode emission. 37 Although a side-mode suppression ratio of 30 dB has been reported from this design, frequency tuning from this device has not been reported.
In this work, we exploit the spectral engineering offered by defect sites in laser cavities to control comb spacing and finesse in coupled-cavity terahertz lasers. Defect sites perturb the gain in a laser cavity, resulting in a periodic modulation of the spectral envelop. A series of these defects result in a summation of all mode modulations, emanating from individual defect sites. 38,39 Traditionally, the position of the defect sites are precisely controlled to suppress longitudinal modes and to demonstrate single-mode emission, from a single laser cavity (Figure 1c). 20,39 However, there exist a tremendous flexibility for an engineering of emission characteristics of a laser cavity by simply displacing the location of the defects sites. Recently, we demonstrated the possibility of engineering emission frequencies in a single cavity terahertz QCL by simply displacing the location of a periodically arranged defect sites forming a finite photonic lattice structure. We observed switchable dual frequency operation and controlling comb spacing of longitudinal modes by simply rearranging the location of the defect sites ( Figure 1d). 21 Here, we have patterned one of the cavities in a coupled-cavity terahertz QCL with a multimode defect lattice with a central π-phase shifted defect to control finesse and longitudinal mode separation (Figure 1e), much like those obtained from more complex designs such as SG-DBR but using much shorter cavities, suitable for operation at terahertz frequencies. We report both wideband mode-hops and mode-hop-free continuous tuning through Vernier selection. The emission frequencies are tuned by exploiting the Stark shift of the material gain, cavity pulling effects, localized Joule heating, and thermal coupling between cavities. We demonstrate frequency tuning over 180 GHz at a fixed heat sink temperature of 50 K. This extends to 209 GHz tuning, including mode-hop free continuous tuning over 6−21 GHz for variable heat sink temperatures. The side mode suppression ratio is in the range ∼20−40 dB. The frequency tuning range reported here is the highest obtained through electrical and thermal control in a terahertz QCL, without any external mechanical control.

■ DEVICE DESIGN
A coupled-cavity QCL comprising of a longer cavity (cavity 1) and a shorter cavity (cavity 2) separated by an air gap was used in this study. A schematic diagram of the terahertz QCL is shown in Figure 2. A photonic lattice was designed to be patterned on to cavity 1 only using the design methodology described in ref 21.
The design steps are (1) simulation of optical modes in the terahertz QCL with and without any cladding metal forming the photonic lattice; (2) calculation of photonic lattice periodicity as a first approximation; (3) transfer matrix simulation of the coupled-cavity QCL with and without the photonic lattice; and (4) optimization of the design using an iterative algorithm to vary the displacement and duty cycle of

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pubs.acs.org/journal/apchd5 Article the photonic lattice to obtain a multimode the emission from cavity 1. The optical mode in the terahertz QCL was simulated using COMSOL Multiphysics to calculate the refractive index of the fundamental mode and to design the photonic lattice to be patterned on cavity 1. A 60 μm wide narrow ridge was used to preserve the fundamental transverse mode, as well as to reduce the input electrical power to the devices. The effective refractive index of the optical mode was found to be n eff,m = 3.6467. A photonic lattice etch depth of 4 μm was computed to provide an index contrast Δn eff = 0.6389. The first-order Bragg wavelength (λ BR ) was used to calculate the lengths of the metallized (L m ) and the etched sections (L e ) of the photonic lattice as a function of the duty cycle (σ), using the following expressions: In the first instance, an approximate value of the periodicity of the photonic lattice was calculated. A Bragg wavelength of λ BR = 87.219 μm (frequency f BR = 3.437 THz) and duty cycle of cycle σ = 0.7 was selected, resulting in calculated lengths of the metallized and the etched sections of the photonic lattice to be L m = 8.37 μm and L e = 4.35 μm, respectively. The periodicity of the photonic lattice was Λ = L m + L e = 12.72 μm.
Whereas photonic lattices are usually patterned in the center of a cavity to obtain single-mode emission, varying the position of the lattice in the cavity modifies the emission characteristics. 21 As such, the position of the lattice was displaced to modify the transmission properties of cavity 1. The transmission and spectral behavior of the coupled-cavity device with/without any photonic lattice was simulated using a transfer matrix model.
Transfer Matrix Model. The transmission characteristics of the device describing the propagation of the electric field were modeled using transfer matrices. 21,33,36 The matrix elements of a defect site are defined as where t and r are the transmission and reflection coefficients calculated from the complex refractive indices of the fundamental mode; φ + = β m L m + β e L e and φ − = β m L m − β e L e , where β m and β e are complex propagation constants in the metallised and etched sections of the photonic lattice (calculated from the COMSOL model). The photonic lattice was modeled by cascading N iterations of the single defect site on either side of a central π-phase shifted defect of length 2 × L e . The center of the photonic lattice was offset from the center of cavity 1 by a distance δ, resulting in an asymmetry of the cavity 1 length on either side of the photonic lattice. We define the cavity 1 lengths from the front facet to the photonic lattice to be L F and that from the lattice to the air gap to be L R . The transmission through the entire device was modeled as where T F and T R are the transfer matrices of cavity 1 before and after the photonic lattice, T pi is the transfer matrix of the central π-phase shifted defect of length 2 × L e , and T air and T 2 are the transfer matrices of the air gap and cavity 2, respectively. An iterative algorithm was written to systematically vary the photonic lattice parameters (L m , L e , and δ) and to calculate the emission properties from the device such that a multimode emission is obtained from cavity 1. In order to simulate frequency tuning properties, the transfer matrix model also included drive current dependent gain in both cavities (calculated from a Schrodinger-Poisson solver), thermal coupling between cavities (calculated using finite element modeling), 34 and waveguide dispersion. The transfer matrix model was used to simulate emission characteristics of a 5.4 mm long QCL (with a material gain centered at ∼3.55 THz 40 ) that was selected for this work. An air gap was patterned using focused ion beam milling to form two optically coupled-cavities the lengths of which were selected such that the longitudinal modes from the two cavities are resonant at multiple frequencies. This was done deliberately to verify the operation of the defect engineered lattice. To achieve this, the cavity lengths were chosen to be 3.75 mm (cavity 1) and 1.65 mm (cavity 2), separated by a 10 μm wide air gap, such that the ratio between the cavity lengths is >2. Normalized transmission spectra of individual cavities are shown in Figure 3a. The transmission peaks from both cavities are spaced at a ratio of 2.27. The free spectral range of cavities 1 and 2 were calculated from the transmission peaks simulated using a transfer matrix model to be 10.89 and 24.75 GHz, respectively.
A defect engineered photonic lattice was then designed using the iterative algorithm to modify the spectral characteristics of cavity 1, and to improve the frequency emission and tuning characteristics from the device. A photonic lattice with eight defect sites on either side of a central π-phase shifted defect was designed such that a Vernier resonance is realized at the peak of the gain spectrum (∼3.55 THz). For simplicity, the periodicity of the photonic lattice was kept constant at Λ = 12.72 μm, while the lattice parameters L m , L e , and δ were varied. The lengths of the metallized and etched sections of the Figure 2. Schematic diagram of the coupled-cavity terahertz QCL with a defect engineered photonic lattice used in this work. The lattice is patterned on to the longer cavity (cavity 1, red). The shorter cavity (cavity 2, blue) is coupled to cavity 1 through an air-gap.

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pubs.acs.org/journal/apchd5 Article photonic lattice required to achieve this was calculated to be L m = 8.9 μm and L e = 3.82 μm. A central π-phase shifted defect (etched section) of length 2 × L e = 7.64 μm was also included in the photonic lattice. The center of the photonic lattice was offset from the center of cavity 1 by δ = 36.1 μm, such that L F > L R . Simulated normalized transmission from cavity 1 with the photonic lattice is shown in Figure 3b. The photonic lattice increases the free spectral range of cavity 1 to ∼21 GHz, thereby reducing the ratio of mode separation between the cavities from 2.27 to 1.19 and disrupting the resonance at multiple frequencies so that only the resonance at ∼3.55 THz remains. The finesse (F) of the cavity 1 mode at ∼3.55 THz, calculated from a ratio of the free spectral range (Δλ) and the full-width-half-maximum bandwidth (δλ), increased from ∼2.75 (without photonic lattice) to ∼3.5 (after photonic lattice), corresponding to an increase in the reflectivity from ∼36% to ∼46%. In this modified coupled cavity, mode hops are expected at ∼20 GHz intervals.
Frequency Tuning. The emission frequency is controlled through a combination of Stark shift of gain, cavity pulling effects, and thermal effects through localized Joule heating, thermal coupling between cavities, and by varying the heat sink temperature.
The Stark shift of the gain was calculated from the electric field (F) applied across the QCL, using the relation: 35 where Ψ 1 and Ψ 2 are the wave functions of the lower and upper laser levels, calculated using a Schrodinger−Poisson solver, and e is the elementary charge. The Stark shift was calculated from the dynamic operating range of the QCL to be ΔE S = 2.64 meV, for a change in applied field ΔF = 6 kV/cm (agreeing well with the reported values of 4−6 kV/cm), 40 corresponding to a change in terminal voltage of ΔV = 8.5 V. From this, the Stark shift as a function of applied electric field was calculated dE S /dV = 0.504 meV/V, and the coefficient of a change in refractive index is reported to be dn/dV = 0.0021 V −1 for the QCL material used in this study 35 and was used in the transfer matrix model. The Stark shift arising from the diagonal transition in the QCL material allows us to further increase in tuning range by driving cavity 2 above lasing threshold and varying the gain by changing the current. 41 In this configuration, since both cavities are operating above the lasing threshold, gain is distributed between the two cavities. The frequency dependent gain in the QCL cavity results in a dispersion of the real part of the refractive index arising through Kramer−Kronig relationship. 42 This frequency-dependent dispersion was used to change the refractive index in the coupled-cavity QCL through cavity pulling effects, where the gain in cavities 1 and 2 are varied independently. 35,43 Since both cavities are driven above threshold, the perturbation of the index in the coupled-cavity QCL depends on the relative gain and Stark shift in each cavity. The dispersion at each eigenmode, simulated from the transfer matrix model, was calculated as a function of the electric field at each cavity. The amplitude of the electric field was varied throughout the dynamic range of each cavity. The change in refractive index due to the Stark shift in gain and cavity pulling was calculated to be −14 × 10 −3 ≤ Δn C ≤ 14 × 10 −3 , at 3.55 THz and at a heat sink temperature of 10 K.
Refractive index was also perturbed using localized Joule heating using wide current pulses. The normalized thermal resistance of the QCL was calculated to be R TH * = 20 K cm W 1 , and the coefficient of thermal change in refractive index was calculated to be dn/dT = 1 × 10 −4 K 1 from reference devices. A change in the refractive index of Δn T = 10 × 10 −3 was calculated when the heat sink temperature is changed by 100 K.
The change in the lattice temperature was calculated from the input electrical power and was used to estimate the change in refractive index through electrical heating. The maximum change in input electrical power during dynamic operating range for both cavities was calculated to be ∼9.8 W (ΔV = 8.5 V, change in drive current of 0.35 and 0.8 A for cavities 1 and 2, respectively). This results in a change of refractive index of Δn P = 18.5 × 10 −3 associated with a current pulse train with 95% duty cycle. The transfer matrix model was modified to include refractive index perturbation through a combination of Stark shift, cavity pulling and thermal heating. To this end, the fields across both cavities were simulated to be varied across the dynamic operating range at pulse widths in the range of 2−95 μs (periodicity 100 μs), and at heat sink temperatures in the range 10−110 K. The range of refractive index change through these approaches was calculated to be −22.5 × 10 −3 < Δn eff < 22.5 × 10 −3 . Emission in real experiments was collected from the front facet of cavity 1. As such, the matrix model was also modified to account for this asymmetric cavity and the additional propagation length in such drive conditions when the cavity 1 is switched off.
The simulated transmission properties from the defect engineered coupled-cavity QCL is plotted as a function of net variations (Δn eff = n eff,1 − n eff,2 ) in the effective refractive index (Figure 4). There are mode-hops between 8 frequency bands spanning ∼3.49−3.62 THz, with a frequency separation of ∼20 GHz. A mode-hop free continuous frequency tuning of ∼8−13 GHz was also simulated across six of the frequency bands. The total tuning range was found to be in the range ∼170−180 GHz, more than half the gain bandwidth of ∼250 GHz provided by the active region in a Fabry-Peŕot cavity.

■ FABRICATION
A terahertz QCL, based on an active region reported by Wienold et al. in ref 40 was rescaled to operate at frequencies 3.4−3.7 THz and was used for this study. The QCL was grown using molecular beam epitaxy using GaAs/Al 0.18 Ga 0.82 As material system. Initially, a 250 nm thick GaAs buffer layer,  The packaged device was etched using a dual beam focused ion-beam system (FEI Nova 200 NanoLab) initially to form a 10.88 μm wide air gap separating the 3.74 mm long cavity 1 and the 1.67 mm long cavity 2. Later, a photonic lattice with Λ = 12.72 μm, L e = 3.82 μm, and L m = 8.9 μm was patterned using focused ion beam milling on cavity 1. The center of the photonic lattice was offset from the center of cavity 1 by 36.1 μm.

■ EXPERIMENTAL RESULTS
The QCL was characterized in a Janis ST-100 continuous flow helium-cooled cryostat. Both the cavities were driven with 10 kHz quasi-DC pulses with variable pulse-widths. Radiation was collected from the front facet of cavity 1 in all instances. Time averaged power was measured using a Ge:Ga photodetector and calibrated using a Thomas Keating power meter. Spectra were acquired using a Bruker Fourier transform infrared spectrometer with a resolution of 7.5 GHz. All experimental data are openly accessible from ref 44.
Power Output. The light−current−voltage characteristics of each cavity (with the other switched off) were recorded at different heat sink temperatures (Figure 5a,b). A peak output power of 3.5 and 1.25 mW was measured from cavities 1 and 2, respectively. The total output power was also measured as the current amplitudes were varied simultaneously in both cavities (Figure 5c−f). An increase in the emitted power was recorded when both cavities are driven above threshold, with a maximum power of 4 mW at a heat sink temperature of 10 K.
Spectral Characterization. In the first instance, spectra were acquired by driving each cavity above threshold using 2 μs wide pulses, with the other cavity switched off. The single mode emission hops to higher frequencies as a function of current amplitude, due to the Stark shift of gain (Figure 6a−d). The frequency separation between the modes were measured to be in the range ∼19−20 GHz and agrees well with the simulated value of ∼20 GHz. Increasing the width of the current pulses increases the ambient lattice temperature, allowing a continuous tuning of the emission frequency in the range ∼1−1.5 GHz when pulse widths are varied in the range 2−95 μs. A variation in the peak emission frequency as a function of pulse widths at different current amplitudes and at a heat sink temperature of 70 K is shown in Figure 6e. A modehop free continuous tuning over ∼5−6 GHz across narrow bands of frequencies is recorded through changes in drive current amplitudes, pulse widths, and heat sink temperatures (Figure 6e,f). The results obtained here agrees well with similar results obtained from single cavity photonic lattice QCLs. 21 We note that the long electrical pulses do not result in any slow transient changes in frequency as the pulse duration used in these measurements are much longer than the time required for a single-mode to establish from transient multimodes (stabilization time of coupled-cavity terahertz QCLs are measured to be ∼1.5 ns 45 ).
Spectra were similarly recorded when drive amplitude and widths of the current pulses to both cavities were varied systematically. Data recorded at a heat sink temperature of 50 K is shown in Figure 7. Mode-hop occurs between four modes when the current amplitude at cavity 2 was varied and cavity 1 was invariant (Figure 7a). The frequency tuning observed here is due to both Stark shift of gain and cavity pulling effect, and is not a superposition of emission frequencies when the cavities operated independently. This is verified by comparing the spectra to those recorded from cavity 2 alone. Frequency tuning is also controlled through thermal perturbation. Both

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pubs.acs.org/journal/apchd5 Article mode-hops and hop-free continuous tuning was observed through a variation of pulse widths, when drive conditions in cavity 1 were invariant (Figure 7b,c). A continuous frequency tuning through thermal effects was also observed by varying pulse widths in both cavities simultaneously, while all other drive parameters remained constant (Figure 7d). Through such a systematic variation of the drive parameters, mode hops over 180 GHz (from ∼3.48−3.66 THz) and mode hop-free continuous tuning in the range ∼1−4.8 GHz was recorded at a heat sink temperature of 50 K (Figure 7e). These results are the best fast frequency tuning performance from a terahertz QCL without the need for any slow control processes like    (Figure 8b−g). Although the experimentally recorded emission frequencies are ∼10 GHz lower than those simulated, the spectral coverage agrees well with the tuning range simulated from the transfer matrix model. The continuous tuning of ∼21 GHz between ∼3.56−3.58 THz shows complete frequency coverage between two discrete frequency bands and agrees well with the continuous tuning of ∼13 GHz simulated at 3.57 and 3.59 THz.
We note that frequency tuning is not controlled as a function of monotonic change of a single tuning parameter. Nevertheless, a look-up table containing peak frequencies was created to allow a programmable tuning source using appropriate instrumentation to control the electrical drive parameters, similar to the tuning control used in multisection diode lasers. While the slow heat sink temperature based control may not ideal for every application, there are many situations where frequency tuning speeds are not critical. We note that while the frequency coverage is comparable to those obtained from more advanced SG-DBR designs used in midinfrared and diode lasers, the performance of these devices can be further improved by using a broadband QCL material 6 and coating the facets with antireflection coating. 46 We further note that the changes in drive currents to tune the emission frequency also results in a change in output power from the device, which could be mitigated by integrating an optical amplifier. 47 Finally, although the frequency tuning reported here is predominantly based on mode-hops, a mode-hop free continuous tuning can be realized by reducing the facet reflections. However, antireflection coatings required for terahertz frequencies are more than 10 μm thick and the fabrication of such coatings are nontrivial. An alternative approach to avoid facet reflections is to couple multiple microresonators 48 using Y-branches. 35 In such a design, each microresonator can be further patterned with a photonic lattice to form a single unit repetition of a SG-DBR in a closed loop and realize a wideband continuous Vernier tunable terahertz QCL.

■ CONCLUSIONS
A photonic lattice is integrated on to one of the cavities in a coupled-cavity terahertz QCL to modify the comb characteristics of that cavity, similar to SG-DBR designs used in nearand mid-infrared lasers. Vernier frequency tuning from such a device is demonstrated through a combination of Stark shift, cavity pulling effect and thermal perturbation through Joule heating. Using a combination of such effects, fast frequency tuning over 180 GHz (including mode hop-free continuous tuning in the range ∼1−4.8 GHz) is demonstrated at a constant heat sink temperature of 50 K. The frequency range from the device further improved by varying the heat sink temperature to obtain a frequency tuning over 209 GHz (including continuous tuning in the range 6−21 GHz), with side mode suppression of 20−40 dB. A comprehensive database of the spectral emission was created by varying the various control parameters to build a look-up table of emission frequencies. Using this technique, the performance of devices can be further improved by using a heterogeneous active regions 49   The Engineering and Physical Sciences Research Council, UK ("COTS" and "HyperTerahertz" Programmes, EP/J017671/1 and EP/P021859/1); the Royal Society and the Wolfson Foundation.